Numerical Simulation of the Water Entry of Two-Dimensional Body with Flow Separation

2011 ◽  
Vol 138-139 ◽  
pp. 376-381 ◽  
Author(s):  
Yun Bo Li ◽  
Ya Jun Li ◽  
Yan Wang
Keyword(s):  
Free Surface ◽  
Flow Separation ◽  
Water Entry ◽  
Two Dimensional ◽  
Numerical Result ◽  
Runge Kutta Method ◽  
Theory Result ◽  
The Stability ◽  
Stability And Accuracy ◽  
Good Agreement

The water entry of two-dimensional body with flow separation is simulated based on potential theory and boundary element method. The double point model and four-order Runge-Kutta method and jet-cut model and free surface smooth technique and regrinding technique are used to assure the stability and accuracy of the numerical result. A flow separation model is introduced to simulate the water entry of two-dimensional body with knuckle. The free surface elevation and pressure distribution of wedge with knuckle are predicted and compared with other theory result. Good agreement between numerical result and other theory result is indicated that the numerical method is stability and effective.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

On the Hydrodynamic Interaction Between Ship and Free-Surface Motions on Vessels With Moonpools

2019 ◽  
Author(s):  
Senthuran Ravinthrakumar ◽  
Trygve Kristiansen ◽  
Babak Ommani
Keyword(s):  
Free Surface ◽  
Flow Separation ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Navier Stokes ◽  
Linear Potential ◽  
Two Dimensional ◽  
Sloshing Mode ◽  
Vessel Motion

Abstract Coupling between moonpool resonance and vessel motion is investigated in two-dimensional and quasi three-dimensional settings, where the models are studied in forced heave and in freely floating conditions. The two-dimensional setups are with a recess, while the quasi three-dimensional setups are without recess. One configuration with recess is presented for the two-dimensional case, while three different moonpool sizes (without recess) are tested for the quasi three-dimensional setup. A large number of forcing periods, and three wave steepnesses are tested. Boundary Element Method (BEM) and Viscous BEM (VBEM) time-domain codes based on linear potential flow theory, and a Navier–Stokes solver with linear free-surface and body-boundary conditions, are implemented to investigate resonant motion of the free-surface and the model. Damping due to flow separation from the sharp corners of the moonpool inlets is shown to matter for both vessel motions and moonpool response around the piston mode. In general, the CFD simulations compare well with the experimental results. BEM over-predicts the response significantly at resonance. VBEM provides improved results compared to the BEM, but still over-predicts the response. In the two-dimensional study there are significant coupling effects between heave, pitch and moonpool responses. In the quasi three-dimensional tests, the coupling effect is reduced significantly as the moonpool dimensions relative to the displaced volume of the ship is reduced. The first sloshing mode is investigated in the two-dimensional case. The studies show that damping due to flow separation is dominant. The vessel motions are unaffected by the moonpool response around the first sloshing mode.

Traffic Flow on Gradient Highway and its Stability

2011 ◽  
Vol 97-98 ◽  
pp. 877-882 ◽  
Author(s):  
Wen Xing Zhu ◽  
Rui Ling Yu ◽  
Zhi Ping Jia
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Linear Stability Theory ◽  
Stability Conditions ◽  
Traffic Flow Model ◽  
Flow Simulations ◽  
Numerical Result ◽  
The Stability ◽  
Real Traffic ◽  
Good Agreement

In this paper we investigated the stability of the traffic flow on a single lane gradient (uphill/downhill) highway. The linear stability theory was used to analyze the model and get the stability conditions. The theoretical result shows that the slope of the gradient has an influence on the stability of traffic flow. Simulations are carried out to check the slope effect of the traffic flow model. Numerical result is in good agreement with the real traffic situations.

Free Fall Water Entry of a Two-Dimensional Asymmetric Wedge in Oblique Slamming: A Numerical Study

2020 ◽  
Author(s):  
Saeed Hosseinzadeh ◽  
Mohammad Izadi ◽  
Kristjan Tabri
Keyword(s):  
Numerical Study ◽  
Experimental Studies ◽  
Free Fall ◽  
Water Entry ◽  
Vertical Acceleration ◽  
Two Dimensional ◽  
Pile Up ◽  
Real Phenomenon ◽  
Precise Simulation ◽  
Good Agreement

Abstract This paper examines the hydrodynamic problem of a two-dimensional symmetric and asymmetric wedge water entry through freefall motion. The gravity effect on the flow is considered and because of precise simulation close to the real phenomenon, the oblique slamming is analyzed. The defined problem is numerically studied using SIMPLE and HRIC schemes and by implementing an overset mesh approach. In order to evaluate the accuracy of the numerical model, the present results are compared and validated with previous experimental studies and showed good agreement. The results are presented and compared for each symmetry and asymmetry in different deadrise angles, drop heights and heel angles. Based on a comparison of the measured vertical acceleration of the experimental wedge data, it is determined that the proposed numerical method has relatively good accuracy in predicting the slamming phenomenon and wedge response. The influence of viscous regime on water entry simulations is investigated, in according to results, effect of viscosity is negligible. Results show that the heel angle dramatically affects the wedge dynamics, pile-up evolution, and pressure distribution. These results suggest evidence for a complex interaction between geometric parameters on the water entry of rigid wedges, which could finally develop our understanding of planing vessels operating in real sea conditions.

A BOUNDED FINITE-DIFFERENCE DISCRETIZATION OF A TWO-DIMENSIONAL DIFFUSION EQUATION WITH LOGISTIC NONLINEAR REACTION

2011 ◽  
Vol 22 (09) ◽  
pp. 953-966 ◽  
Author(s):  
J. E. MACÍAS-DÍAZ
Keyword(s):  
Finite Difference ◽  
Traveling Wave ◽  
Approximate Solutions ◽  
Traveling Wave Solution ◽  
Two Dimensional ◽  
Numerical Result ◽  
Dimensional Version ◽  
Finite Difference Discretization ◽  
Difference Discretization ◽  
Good Agreement

In the present manuscript, we introduce a finite-difference scheme to approximate solutions of the two-dimensional version of Fisher's equation from population dynamics, which is a model for which the existence of traveling-wave fronts bounded within (0,1) is a well-known fact. The method presented here is a nonstandard technique which, in the linear regime, approximates the solutions of the original model with a consistency of second order in space and first order in time. The theory of M-matrices is employed here in order to elucidate conditions under which the method is able to preserve the positivity and the boundedness of solutions. In fact, our main result establishes relatively flexible conditions under which the preservation of the positivity and the boundedness of new approximations is guaranteed. Some simulations of the propagation of a traveling-wave solution confirm the analytical results derived in this work; moreover, the experiments evince a good agreement between the numerical result and the analytical solutions.

Acoustic destablilization of vortices

1979 ◽  
Vol 290 (1372) ◽  
pp. 353-371 ◽  
Keyword(s):  
Boundary Condition ◽  
Growth Rate ◽  
Mach Number ◽  
Acoustic Waves ◽  
Polar Angle ◽  
Inviscid Flow ◽  
Two Dimensional ◽  
Low Mach Number ◽  
The Stability ◽  
Good Agreement

A line vortex which has uniform vorticity 2Ω 0 in its core is subjected to a small two-dimensional disturbance whose dependence on polar angle is e imθ . The stability is examined according to the equations of compressible, inviscid flow in a homentropic medium. The boundary condition at infinity is that of outgoing acoustic waves, and it is found that this capacity to radiate leads to a slow instability by comparison with the corresponding incompressible vortex which is stable. Numerical eigenvalues are computed as functions of the mode number m and the Mach number M based on the circumferential speed of the vortex. These are compared with an asymptotic analysis for the m = 2 mode at low Mach number in which it is found that the growth rate is (π/ 32) M 4 Ω 0 in good agreement with the numerical results.

MODELLING WATER ENTRY OF A WEDGE BY MULTIPHASE SPH METHOD

2011 ◽  
Vol 1 (32) ◽  
pp. 10 ◽  
Author(s):  
Kai Gong ◽  
Benlong Wang ◽  
Hua Liu
Keyword(s):  
Water Entry ◽  
Computational Domain ◽  
Two Dimensional ◽  
Hydrodynamic Problem ◽  
Sph Method ◽  
Two Phase ◽  
Boundary Treatment ◽  
Sph Model ◽  
Reflection Boundary ◽  
Good Agreement

The hydrodynamic problem of two-dimensional wedge entering water is studied based on SPH model. A non-reflection boundary treatment for SPH method is proposed to reduce the size of computational domain. The details of water entry and enclosing are simulated using two phase SPH model. Both the water flow around the cavity and wedge and air flow inside the cavity are predicted simultaneity. Good agreement is obtained comparing experimental data in terms of both the hydrodynamics force exerting on the wedge and geometry of the cavity and jet.

The stability and transition of a two-dimensional jet

1960 ◽  
Vol 7 (1) ◽  
pp. 53-80 ◽  
Author(s):  
Hiroshi Sato
Keyword(s):  
Laminar Flow ◽  
Numerical Solutions ◽  
Two Dimensional ◽  
Eigenvalues And Eigenfunctions ◽  
Response Characteristics ◽  
Laminar Jets ◽  
The Stability ◽  
Linear Disturbance ◽  
Good Agreement ◽  
Small Disturbances

A study was made of the transition of a two-dimensional jet. In the region where laminar flow becomes unstable, two kinds of sinusoidal velocity fluctuation have been found; one is symmetrical and the other is anti-symmetrical with respect to the centre line of the jet. The fluctuations grow exponentially at first and develop into turbulence without being accompanied by abrupt bursts or turbulent spots.The response characteristics of laminar jets to artificial external excitation were investigated in detail by using sound as an exciting agent. The effect of excitation was seen to be most remarkable when the frequency of excitation coincides with that of self-excited sinusoidal fluctuations.Numerical solutions of equation of small disturbances superposed on laminar flow were obtained assuming the Reynolds number as infinity. Theoretical eigenvalues and eigenfunctions are in good agreement with experimental results, thus verifying the existence of a region of linear disturbance in the two-dimensional jet.

The stability of a two-dimensional laminar jet

1958 ◽  
Vol 4 (3) ◽  
pp. 261-275 ◽  
Author(s):  
T. Tatsumi ◽  
T. Kakutani
Keyword(s):  
Reynolds Number ◽  
Basic Assumption ◽  
Wave Number ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Lower Branch ◽  
Laminar Jet ◽  
Numerical Result ◽  
The Stability ◽  
Different Parts

This paper deals with the stability of a two-dimensional laminar jet against the infinitesimal antisymmetric disturbance. The curve of the neutral stability in the (α, R)-plane (α, the wave-number; R, Reynolds number) is calculated using two different methods for the different parts of the curve; the solution is developed in powers of (αR)−1 for obtaining the upper branch of the curve and in powers of αR for the lower branch.The asymptotic behaviour of these branches is that for branch I,$\alpha \rightarrow 2, \;\; c \rightarrow \frac{2}{3}$ for $R \rightarrow \infty$; and for branch II, $R \sim 1\cdot12\alpha^{-1|2},\; c \sim 1\cdot 20 \alpha^2$ for α → 0. Some discussion is given on the validity of the basic assumption of the stability theory in relation to the numerical result obtained here.

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